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Simplifying x2 + 18x + -57 = -8 Reorder the terms: -57 + 18x + x2 = -8 Solving -57 + 18x + x2 = -8 Solving for variable 'x'. Reorder the terms: -57 + 8 + 18x + x2 = -8 + 8 Combine like terms: -57 + 8 = -49 -49 + 18x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -49 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 18x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 18x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 18x + x2 = 0 + 49 18x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 18x + x2 = 49 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 49 + 81 Reorder the terms: 81 + 18x + x2 = 49 + 81 Combine like terms: 49 + 81 = 130 81 + 18x + x2 = 130 Factor a perfect square on the left side: (x + 9)(x + 9) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 9) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 9 = 11.401754251 Simplifying x + 9 = 11.401754251 Reorder the terms: 9 + x = 11.401754251 Solving 9 + x = 11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 11.401754251 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.401754251 + -9 x = 11.401754251 + -9 Combine like terms: 11.401754251 + -9 = 2.401754251 x = 2.401754251 Simplifying x = 2.401754251Subproblem 2
x + 9 = -11.401754251 Simplifying x + 9 = -11.401754251 Reorder the terms: 9 + x = -11.401754251 Solving 9 + x = -11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -11.401754251 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.401754251 + -9 x = -11.401754251 + -9 Combine like terms: -11.401754251 + -9 = -20.401754251 x = -20.401754251 Simplifying x = -20.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.401754251, -20.401754251}
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